{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:M744L6PNDK6EYLTT3MUEPKHY6N","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"dfb826dc9cd22eb5e7430b6a036ae47b8c056c21f750c3dd88c1bfc48be97ea0","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-04-12T15:49:29Z","title_canon_sha256":"c5cf43ca3837c7e321e94a2a2b27357a3c25add3e7d01ed1cc684e4bae9986a4"},"schema_version":"1.0","source":{"id":"1804.04579","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.04579","created_at":"2026-07-05T03:50:45Z"},{"alias_kind":"arxiv_version","alias_value":"1804.04579v3","created_at":"2026-07-05T03:50:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.04579","created_at":"2026-07-05T03:50:45Z"},{"alias_kind":"pith_short_12","alias_value":"M744L6PNDK6E","created_at":"2026-07-05T03:50:45Z"},{"alias_kind":"pith_short_16","alias_value":"M744L6PNDK6EYLTT","created_at":"2026-07-05T03:50:45Z"},{"alias_kind":"pith_short_8","alias_value":"M744L6PN","created_at":"2026-07-05T03:50:45Z"}],"graph_snapshots":[{"event_id":"sha256:99b1e9e2718dfcd9dc20e0d0f95a4df0867a7096bd121169a7545e82f7f847cd","target":"graph","created_at":"2026-07-05T03:50:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1804.04579/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that the product in the quantum K-ring of a generalized flag manifold $G/P$ involves only finitely many powers of the Novikov variables. In contrast to previous approaches to this finiteness question, we exploit the finite difference module structure of quantum K-theory. At the core of the proof is a bound on the asymptotic growth of the $J$-function, which in turn comes from an analysis of the singularities of the zastava spaces studied in geometric representation theory.\n  An appendix by H. Iritani establishes the equivalence between finiteness and a quadratic growth condition on cer","authors_text":"David Anderson, Hiroshi Iritani, Hsian-Hua Tseng, Linda Chen","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-04-12T15:49:29Z","title":"On the finiteness of quantum K-theory of a homogeneous space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.04579","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d74a430dc400f0bf0ce7716ce58561e07dfeb39fab400e44d533c30fde6a190f","target":"record","created_at":"2026-07-05T03:50:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"dfb826dc9cd22eb5e7430b6a036ae47b8c056c21f750c3dd88c1bfc48be97ea0","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-04-12T15:49:29Z","title_canon_sha256":"c5cf43ca3837c7e321e94a2a2b27357a3c25add3e7d01ed1cc684e4bae9986a4"},"schema_version":"1.0","source":{"id":"1804.04579","kind":"arxiv","version":3}},"canonical_sha256":"67f9c5f9ed1abc4c2e73db2847a8f8f346652c25d0c63ec4f1d2ae3453379a79","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67f9c5f9ed1abc4c2e73db2847a8f8f346652c25d0c63ec4f1d2ae3453379a79","first_computed_at":"2026-07-05T03:50:45.382809Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:50:45.382809Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S3x/Klx9xXdiYaRtCUZmtwfH1hMjxtqbTO3yELJuqcdhQraEfXOR1nYJhimGiG+m0jWHF5SQhUrIg24N6fnbCA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:50:45.383224Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.04579","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d74a430dc400f0bf0ce7716ce58561e07dfeb39fab400e44d533c30fde6a190f","sha256:99b1e9e2718dfcd9dc20e0d0f95a4df0867a7096bd121169a7545e82f7f847cd"],"state_sha256":"871db366a01219495d3428da9f22887aad4c710b50d791b3a998e43690dcae19"}